This invention relates generally to oxygen sensing methods and apparatus, and, more particularly, relates to apparatus and methods for measuring oxygen concentration in gas mixtures by magnetic means.
Accurate measurement of oxygen concentration in a gas mixtures is critical to many industrial, clinical and laboratory processes, and a variety of devices have therefore been proposed or developed for measuring oxygen concentration. It has long been recognized that oxygen is paramagnetic, in that its molecules seek the strongest part of a magnetic field. Most other gases, in contrast, are diamagnetic, in that their molecules seek the weakest part of a magnetic field. The widely recognized paramagnetic properties of oxygen have stimulated a number of investigations into methods and apparatus for measuring oxygen concentration in gas mixture by magnetic sensing apparatus.
In particular, if a substance is placed in a magnetic field of strength H, the magnetic induction is given by B, where EQU B=H+4(pi)(zeta) Eq. (1)
where the quantity (zeta) is the intensity of magnetization, and EQU (zeta)/H=k Eq. (2)
is the magnetic susceptibility per unit volume.
Generally, the mass susceptibility of diamagnetic substances is independent of temperature and of field strength. The susceptibility of paramagnetic substances, however, is inversely proportional to the absolute temperature, and independent of field strength. Because the density is also inversely proportional to temperature, the susceptibility by volume is inversely proportional to the square of the temperature.
Any substance placed in a magnetic field develops an induced moment, analogous to the induced electric moment developed by a non-polar molecule in an electric field. A paramagnetic substance, however, has a permanent moment, similar to the permanent electric dipole moment of a polar molecule.
If a body is placed in a uniform magnetic field, it will experience an orienting effect, unless it is magnetically isotropic. The magnetic moment acquired by the body under these circumstances will be proportional to kvH, i.e., the product of volume, susceptibility per unit volume, and field intensity.
However, the body will experience no displacing force if the field is uniform. If the field is non-uniform, with a gradient dH/dS in the direction S, the body will experience a linear displacing force in the direction S, and this linear displacing force F will be given by EQU F=(kvh)(dH/dS) Eq. (3)
that is, the force will be proportional to the product of the moment and the gradient.
If a sample of matter is placed between the poles of a magnet so that one part of the sample is in a region of large field strength and the other is in a region of negligible field, then the force acting on the sample is that described by Equation (3), integrated from the region of maximum field out to the region of negligible field. This integration gives a resultant force EQU F=1/2(kH.sup.2 A) Eq. (4)
where A is the cross sectional area of the sample.
An early type of paramagnetic measuring cell, which relied upon the magnetic susceptibility of oxygen, is described in Pauling, et al, "An Instrument for Determining the Partial Pressure of Oxygen in a Gas", 68 Journal of the American Chemical Society 795, (1946). The Pauling et al measuring cell utilizes a sealed glass tube containing a weakly diamagnetic gas, such as nitrogen. The tube is suspended between the wedge-shaped pole pieces of a permanent magnet, which provide a non-uniform magnetic field, and the tube is free to rotate about a vertical axis. The entire structure is then placed within a chamber containing a selected gas.
When oxygen is introduced into the chamber surrounding the tube, the nitrogen in the tube is effectively diamagnetic relative to the surrounding paramagnetic oxygen gas, and the tube experiences a force tending to rotate it into the region where the magnetic field is weakest.
This rotation, or a force required to prevent this rotation, can be measured as an indication of the concentration of oxygen in the chamber. The Pauling cell, however, is fragile, and the rotational axis of the tube must be consistently oriented for each use, rendering it unsuitable for industrial oxygen measurement applications.
Another type of apparatus for measuring the concentration of oxygen relies upon the inverse relationship between temperature and the magnetic susceptibility of oxygen. To exploit this inverse relationship, a heating element can be used to heat a portion of an oxygen-containing mixture in a non-homogeneous magnetic field, thus creating a "magnetic wind" gas flow that can be measured by its thermal effect on adjacent thermistor elements.
In particular, the magnetic susceptibility of the sample gas is inversely proportional to the square of the temperature, and susceptibility can fall to negligible levels if the heating is sufficient. If the heating element provides incomplete or insufficient heating, however, the magnetic susceptibility of the sample remains significant. Under these circumstances, Equation (3) becomes EQU F=1/2(k-k.sub.o)(H.sup.2 -H.sub.o.sup.2) A Eq. (5)
where k.sub.o is the residual susceptibility and H.sub.o is the residual field intensity.
Various configurations of magnetic wind devices are discussed in Medlock, et al, "Oxygen Analysis", Transactions of the Instruments and Methods Conference, Stockholm, 1949, pp. 1-8; and Ellis, et al, "The Measurement of Gaseous Oxygen Tension Utilizing Paramagnetism", 40 British Journal of Anaesthesia 569 (1968).
Conventional magnetic wind oxygen measurement devices, unfortunately, are subject to relatively large errors due to the changes in the thermal properties of the surrounding, or "background" gases. In particular, the presence of different background gases causes conventional magnetic wind oxygen sensors to yield false readings of oxygen levels, due to the large differences in thermal characteristics of the background gases.
Prior magnetic wind oxygen sensing devices also suffer from position sensitivity and background gas dependency, especially in comparison with methods based on direct measurement of magnetic susceptibility.
Moreover, designers of paramagnetic gas sensors have heretofore assumed--based on the relationship between magnetic field gradient and the force experienced by a sample in a non-homogenous magnetic field--that in order to obtain a strong measurement signal, it is necessary to maintain a high magnetic field gradient and to locate the wind-generating resistance elements in the high gradient zone.
Proceeding on this assumption, certain prior art devices employ magnetic pole pieces shaped so as to generate a localized maximum magnetic field gradient, and utilize heating/sensing thermistors located in the high gradient zone. The heating effect of these thermistors, however, is not confined to the region of highest field intensity, but instead "leaks" into a second zone beyond the region of high field intensity. The elevated temperature reduces magnetic susceptibility in this second zone, and thus reduces the signal generated by the sensing thermistors. The configuration of certain conventional sensing devices, therefore, prevents the attainment of maximum measurement signal.
U.S. Pat. No. 3,064,465 of Richardson is an example of this configuration. The Richardson patent discloses a measurement device in which the magnetic pole pieces are shaped to provide a maximum magnetic gradient, and in which the heating effect of the heating thermistors extends beyond the point of highest field intensity, into the zone where should ideally have the lowest temperature to maximize the measurement signal. This reduction in measurement signal, caused by heating and susceptibility reduction outside of the zone of maximum field intensity, is a significant limitation of the prior art.
It is accordingly an object of the invention to provide oxygen sensing methods and apparatus which yield sensitive, accurate measurements of oxygen concentration, independent of background gas composition and thermal properties.
It is a further object of the invention to provide oxygen measurement apparatus which are rugged, reliable, and readily portable.
Other general and specific objects of the invention will in part be obvious and will in part appear hereinafter.